Capacity and assortment planning under one-way supplier-driven substitution for pharmacy kiosks with low drug demand. (English) Zbl 1430.90571
Summary: MedAvail Technologies Inc. is a healthcare technology company that develops new technologies for self-serve pharmacy solutions. The technology, called MedCenter, is a pharmacy kiosk that provides 24/7, easy, and reliable access to pre-packaged prescription drugs and over the counter medications. To meet its business goals of having the right medication in the right kiosk at the right quantity, MedAvail faces several challenges related to assortment and stocking decisions of medications in the kiosk limited by kiosk capacity. This research addresses these decisions through an analytics project aimed at analyzing pharmaceutical sales, determining optimized kiosk storage capacity and service levels, and recommending assortment, stocking, and supplier-driven product substitution guidelines. We developed several mixed integer optimization models that use sales data to obtain robust solutions with respect to randomness in demand. We perform extensive testing using real as well as randomly generated data, and under multiple substitution rules, replenishment guidelines, and demand prediction strategies. Our results show that supplier-driven product substitution could save up to 9% in storage capacity depending on the desired service level and characteristics of product demand. We also propose a column-generation based heuristic approach that, on average, obtains near optimal solutions within 1.1% of optimality gap while reducing computational times by a factor of three.
MSC:
| 90C90 | Applications of mathematical programming |
| 90C11 | Mixed integer programming |
| 90B05 | Inventory, storage, reservoirs |
References:
| [1] | Aardal, K.; Jonsson, Ö.; Jönsson, H., Optimal inventory policies with service-level constraints, Journal of the operational research society, 40, 1, 65-73 (1989) · Zbl 0673.90028 |
| [2] | Abdel-Aal, M. A.; Syed, M. N.; Selim, S. Z., Multi-product selective newsvendor problem with service level constraints and market selection flexibility, International Journal of Production Research, 55, 1, 96-117 (2017) |
| [3] | Abdel-Malek, L.; Montanari, R.; Morales, L. C., Exact, approximate, and generic iterative models for the multi-product newsboy problem with budget constraint, International Journal of Production Economics, 91, 2, 189-198 (2004) |
| [4] | Abdel-Malek, L. L.; Montanari, R., An analysis of the multi-product newsboy problem with a budget constraint, International Journal of Production Economics, 97, 3, 296-307 (2005) |
| [5] | Agarwal, Y.; Mathur, K.; Salkin, H. M., A set-partitioning-based exact algorithm for the vehicle routing problem, Networks, 19, 7, 731-749 (1989) · Zbl 0682.90050 |
| [6] | Agrawal, R.; Srikant, R., Fast algorithms for mining association rules, Proceedings of the twentieth international conference on very large data Bases, VLDB, 1215, 487-499 (1994) |
| [7] | Ahiska, S. S.; Gocer, F.; King, R. E., Heuristic inventory policies for a hybrid manufacturing/remanufacturing system with product substitution, Computers & Industrial Engineering, 114, 206-222 (2017) |
| [8] | Aydin, G.; Porteus, E. L., Joint inventory and pricing decisions for an assortment, Operations Research, 56, 5, 1247-1255 (2008) · Zbl 1167.90478 |
| [9] | Bagchi, U.; Gutierrez, G., Effect of increasing component commonality on service level and holding cost, Naval Research Logistics (NRL), 39, 6, 815-832 (1992) · Zbl 0825.90514 |
| [10] | Bassok, Y.; Anupindi, R.; Akella, R., Single-period multiproduct inventory models with substitution, Operations Research, 47, 4, 632-642 (1999) · Zbl 0979.90005 |
| [11] | Bertsimas, D.; Thiele, A., A robust optimization approach to inventory theory, Operations research, 54, 1, 150-168 (2006) · Zbl 1167.90314 |
| [12] | Carøe, C. C.; Tind, J., L-shaped decomposition of two-stage stochastic programs with integer recourse, Mathematical Programming, 83, 1-3, 451-464 (1998) · Zbl 0920.90107 |
| [13] | Chand, S.; Ward, J. E.; Weng, Z. K., A parts selection model with one-way substitution, European Journal of Operational Research, 73, 1, 65-69 (1994) · Zbl 0806.90026 |
| [14] | Chen, M.; Chuang, C., An extended newsboy problem with shortage-level constraints, International Journal of Production Economics, 67, 3, 269-277 (2000) |
| [15] | Choi, S.; Ruszczyński, A.; Zhao, Y., A multiproduct risk-averse newsvendor with law-invariant coherent measures of risk, Operations Research, 59, 2, 346-364 (2011) · Zbl 1233.90016 |
| [16] | Deflem, Y.; Van Nieuwenhuyse, I., Managing inventories with one-way substitution: A newsvendor analysis, European Journal of Operational Research, 228, 3, 484-493 (2013) · Zbl 1317.90021 |
| [17] | Desaulniers, G.; Desrosiers, J.; Dumas, Y.; Solomon, M. M.; Soumis, F., Daily aircraft routing and scheduling, Management Science, 43, 6, 841-855 (1997) · Zbl 0890.90057 |
| [18] | Dutta, P.; Chakraborty, D., Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand, European Journal of Operational Research, 200, 1, 99-110 (2010) · Zbl 1188.90008 |
| [19] | Erlebacher, S. J., Optimal and heuristic solutions for the multi-item newsvendor problem with a single capacity constraint, Production and Operations Management, 9, 3, 303-318 (2000) |
| [20] | Ford Jr, L. R.; Fulkerson, D. R., A suggested computation for maximal multi-commodity network flows, Management Science, 5, 1, 97-101 (1958) · Zbl 0995.90516 |
| [21] | Fuller, J. B.; O’Conor, J.; Rawlinson, R., Tailored logistics: the next advantage, Harvard Business Review, 71, 3, 87-98 (1993) |
| [22] | Gaur, V.; Honhon, D., Assortment planning and inventory decisions under a locational choice model, Management Science, 52, 10, 1528-1543 (2006) · Zbl 1232.90050 |
| [23] | Gilmore, P. C.; Gomory, R. E., A linear programming approach to the cutting-stock problem, Operations research, 9, 6, 849-859 (1961) · Zbl 0096.35501 |
| [24] | Gilmore, P. C.; Gomory, R. E., A linear programming approach to the cutting stock problem—part ii, Operations research, 11, 6, 863-888 (1963) · Zbl 0124.36307 |
| [25] | Hadley, G.; Whitin, T. M., Analysis of inventory systems, Technical Report (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J. · Zbl 0133.42901 |
| [26] | HealthcareConference, Medavail technologies inc, Proceedings of the Cowen and company thirty-seventh annual health care conference (2017) |
| [27] | In press. |
| [28] | Jammernegg, W.; Kischka, P., Risk preferences of a newsvendor with service and loss constraints, International Journal of Production Economics, 143, 2, 410-415 (2013) |
| [29] | Khouja, M., The single-period (news-vendor) problem: literature review and suggestions for future research, Omega, 27, 5, 537-553 (1999) |
| [30] | Kök, A. G.; Fisher, M. L., Demand estimation and assortment optimization under substitution: Methodology and application, Operations Research, 55, 6, 1001-1021 (2007) · Zbl 1167.91386 |
| [31] | Kök, A. G.; Fisher, M. L.; Vaidyanathan, R., Assortment planning: Review of literature and industry practice, (Agrawal, N.; Smith, S. A., Retail supply chain management: Quantitative models and empirical studies (2015), Springer US: Springer US Boston, MA), 175-236 |
| [32] | Lau, H.-S.; Lau, A. H.-L., The newsstand problem: A capacitated multiple-product single-period inventory problem, European Journal of Operational Research, 94, 1, 29-42 (1996) · Zbl 0929.90003 |
| [33] | Leachman, R.; Glassey, R., Preliminary design and development of a corporate level production planning system for the semiconductor industry, Proceedings of the 1987 ieee international conference on robotics and automation, 4, pp.710-710 (1987), IEEE |
| [34] | Lin, J.; Ng, T. S., Robust multi-market newsvendor models with interval demand data, European Journal of Operational Research, 212, 2, 361-373 (2011) · Zbl 1237.90016 |
| [35] | MedAvail (2017). medavail.com. MedAvail |
| [36] | Moon, I.; Choi, S., The distribution free continuous review inventory system with a service level constraint, Computers & industrial engineering, 27, 1-4, 209-212 (1994) |
| [37] | Nahmias, S.; Schmidt, C. P., An efficient heuristic for the multi-item newsboy problem with a single constraint, Naval Research Logistics (NRL), 31, 3, 463-474 (1984) · Zbl 0544.90023 |
| [38] | Oğuz, O., Generalized column generation for linear programming, Management Science, 48, 3, 444-452 (2002) · Zbl 1232.90302 |
| [39] | Pentico, D. W., The assortment problem with probabilistic demands, Management Science, 21, 3, 286-290 (1974) · Zbl 0304.90040 |
| [40] | Pentico, D. W., The assortment problem with nonlinear cost functions, Operations Research, 24, 6, 1129-1142 (1976) · Zbl 0343.90053 |
| [41] | Rajaram, K.; Tang, C. S., The impact of product substitution on retail merchandising, European Journal of Operational Research, 135, 3, 582-601 (2001) · Zbl 0989.90050 |
| [42] | Rao, U. S.; Swaminathan, J. M.; Zhang, J., Multi-product inventory planning with downward substitution, stochastic demand and setup costs, IIE Transactions, 36, 1, 59-71 (2004) |
| [43] | Sadowski, W., A few remarks on the assortment problem, Management Science, 6, 1, 13-24 (1959) · Zbl 0995.90559 |
| [44] | Shin, H.; Park, S.; Lee, E.; Benton, W., A classification of the literature on the planning of substitutable products, European Journal of Operational Research, 246, 3, 686-699 (2015) · Zbl 1346.90054 |
| [45] | Slawsky, R., Kiosks in health care 101 (2015), Network Media Group |
| [46] | Taleizadeh, A. A.; Akhavan Niaki, S. T.; Hoseini, V., Optimizing the multi-product, multi-constraint, bi-objective newsboy problem with discount by a hybrid method of goal programming and genetic algorithm, Engineering Optimization, 41, 5, 437-457 (2009) |
| [47] | Taleizadeh, A. A.; Niaki, S. T.A.; Hosseini, V., The multi-product multi-constraint newsboy problem with incremental discount and batch order, Asian Journal of Applied Sciences, 1, 2, 110-122 (2008) |
| [48] | Tryfos, P., On the optimal choice of sizes, Operations Research, 33, 3, 678-684 (1985) · Zbl 0567.90064 |
| [49] | Turken, N.; Tan, Y.; Vakharia, A. J.; Wang, L.; Wang, R.; Yenipazarli, A., The multi-product newsvendor problem: Review, extensions, and directions for future research, Handbook of newsvendor problems, 3-39 (2012), Springer |
| [50] | Vairaktarakis, G. L., Robust multi-item newsboy models with a budget constraint, International Journal of Production Economics, 66, 3, 213-226 (2000) |
| [51] | Waring, A. C., Risk-averse selective newsvendor problems, PhD Dissertation (2012), University of Michigan |
| [52] | Wollmer, R. D., An airline seat management model for a single leg route when lower fare classes book first, Operations research, 40, 1, 26-37 (1992) · Zbl 0825.90664 |
| [53] | Zhang, B.; Xu, X.; Hua, Z., A binary solution method for the multi-product newsboy problem with budget constraint, International Journal of Production Economics, 117, 1, 136-141 (2009) |
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